With formula this gets hard

Calculus Level 2

If CC is the curve defined by x(t)=cos2(t)x(t)=\cos^2(t) and y(t)=sin2(t)y(t)=\sin^2(t). The side length of CC for t[0,π2]t\in [0,\frac{\pi}{2}] is in the form a\sqrt{a}. Find the value of aa

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